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Towards a Methodology for Ontology Based Model Engineering Towards a methodology for ontology based model engineering Nicola Guarino and Christopher Welty† LADSEB/CNR Padova, Italy {guarino,welty}@ladseb.pd.cnr.it http://www.ladseb.pd.cnr.it/infor/ontology/ontology.html Phone: +39 049 829 57 51 Fax: +39 049 829 57 63 † on sabbatical from Vassar College, Poughkeepsie, NY Abstract The Formal Tools of Ontological Analysis The philosophical discipline of Ontology is evolving towards an engineering discipline, and in this evolution the Our methodology is based on four fundamental ontologi- need for a principled methodology has clearly arisen. In cal notions, which will be discussed in this section: identity, this paper, we briefly discuss our recent work towards devel- unity, rigidity, and dependence. We shall represent the oping a methodology for ontology-based model engineering. behavior of a property with respect to these notions by This methodology builds on previous methodology efforts, means of a set of meta-properties. Our goal is to show how and is founded on important analytic notions that have been these meta-properties impose some constraints on the way drawn from Philosophy and adapted to Engineering: identity, subsumption is used to model a domain. unity, rigidity, and dependence. We demonstrate how these techniques can be used to analyze properties, which clarifies many misconceptions about taxonomies and helps bring substantial order to ontologies. Preliminaries Let’s assume we have a first-order language L0 (the model- Introduction ing language) whose intended domain is the world to be modeled, and another first order language (the meta-lan- Ontologies are becoming increasingly popular in prac- L1 tice, and the number of poor quality ontologies have made guage) whose constant symbols are the predicates of L0. clear the need for a principled methodology for building Our meta-properties will be represented by predicate sym- them. Perhaps the most common problem we have seen in bols of L1. Primitive meta-properties will correspond to practice with ontologies is that, while they are expected to axiom schemes of L0. When a certain axiom scheme holds bring order and structure to information, their taxonomic in L0 for a certain property, then the corresponding meta- structure is often poor and confusing. This is typically property holds in L1. This correspondence can be seen as a exemplified by the unrestrained use of subsumption to system of reflection rules between L and L , which allow accomplish a variety of reasoning and representation tasks. 0 1 us to define a particular meta-property in our meta-lan- For example, in previous work (Guarino, 1999) several unclear uses of the is-a relation in existing ontologies were guage, avoiding a second-order logical definition. Meta- identified, such as: properties will be used as analysis tools to characterize the ontological nature of properties in L0, and will always be 1. a physical object is an amount of matter (Pangloss) defined with respect to a given conceptualization. 2. an amount of matter is a physical object (WordNet) We shall denote primitive meta-properties by bolded let- This striking dissimilarity poses a difficult integration prob- ters preceded by the sign “+”, “-” or “~” corresponding to lem, since the standard approach of generalizing overlap- carrying the meta-property, not carrying the meta-property, ping concepts would not work, and shows that even the and anti the meta-property. The latter will be used to denote most experienced modelers need some guidance for using special restrictions that are stronger than the simple nega- subsumption consistently. tion, and will be described in more detail, when relevant, In this paper we show how a rigorous analysis of the for each meta-property. We use the notation φM to indicate ontological meta-properties of taxonomic nodes can help φ using the subsumption relation in a disciplined way. These that the property has the meta-property M. meta-properties are based on the philosophical notions of We shall furthermore adopt a first order logic with iden- rigidity, identity, unity, and dependence. They impose some tity. This will be occasionally extended to a simple tempo- constraints on the subsumption relation that clarify many ral logic, where all predicates are temporally indexed by misconceptions about taxonomies – misconceptions that means of an extra argument. If the time argument is omitted normally turn taxonomies into a tangled mess. We discuss for a certain predicate φ, then the predicate is assumed to be these misconceptions by means of real examples, and show time invariant, that is ∃tφ()xt, →∀t φ()xt, . Note that the how our analysis can bring true order to taxonomies, facili- identity relation will be assumed as time invariant: if two tating their understanding, comparison and integration. things are identical, they are identical forever. This means This is a first step towards a general methodology for ontol- that Leibniz’s rule holds with no exceptions. ogy-driven conceptual analysis (ODCA) which combines the established tradition of formal ontology in Philosophy We also adopt a time-indexed mereological relation with the needs of information systems design. P(x,y,t), meaning that x is a (proper or improper) part of y at time t, satisfying the minimal set of axioms and definitions change, and which must not? And how can we reidentify an (adapted from (Simons, 1987), p. 362) shown in Table 1. instance of a certain property after some time? The former issue leads to the notion of rigidity, discussed below, while ∧ ¬ = (proper part) PP(x,y,t) =def f(x,y,t) x y the latter is related to the distinction between synchronic ∃ ∧ O(x,y,t) =def z(P(z,x,t) P(z,y,t)) (overlap) and diachronic identity. An extensive analysis of these P(x,y,t) → E(x,t) ∧ E(y,t) (actual existence of parts) issues in the context of conceptual modeling has been made P(x,y,t) ∧ P(y,x,t) → x=y (antisymmetry) elsewhere (Guarino & Welty, 2000b). P(x,y,t) ∧ P(y,z,t) → P(x,z,t) (transitivity) Finally, it is important to note that, while we use exam- PP(x,y,t) → ∃z(PP(z,y,t) ∧ ¬O(z,x,t)) (weak supplementation) ples to clarify the notions central to our analysis, the exam- ples are not the point of this paper. The everyday use of Table 1. Axiomatization of the part relation. these analysis tools ultimately depend on the assumptions Our domain of quantification will be that of possibilia. resulting from our conceptualization of the world (Guarino, That is, the extension of predicates will not be limited to 1998). For example, the decision as to whether a cat what exists in the actual world, but to what exists in any remains the same cat after it loses its tail, or whether a possible world (Lewis, 1983). For example, a predicate like statue is identical with the marble it is made of, are ulti- “Unicorn” will not be empty in our world, although no mately the result of our sensory system, our culture, etc. instance has actual existence there. Actual existence is The aim of the present analysis is to clarify the formal tools therefore different from existential quantification (“logical that can both make such assumptions explicit, and reveal existence”), and will be represented by the temporally the logical consequences of them. When we say, e.g. that indexed predicate E(x,t), meaning that x has actual exist- “having the same fingerprint” may be considered an iden- ence at time t (Hirst, 1991). tity criterion for PERSON, we do not mean to claim this is the universal identity criterion for PERSONs, but that if this Finally, in order to avoid trivial cases in our meta-prop- were to be taken as an identity criterion in some conceptu- erty definitions, we shall implicitly assume the property alization, what would that mean for the property, for its variables as restricted to discriminating properties instances, and its relationships to other properties? (Guarino, Carrara & Giaretta, 1994), i.e. properties P such that ¸∃xP() x ∧¸∃xP¬()x. Rigidity The Basic Notions A rigid property has been defined in (Guarino, Carrara & The notion of identity is at the core of our methodology. Giaretta, 1994) as a property that necessarily holds for all Despite its fundamental importance in Philosophy, it has its instances. For example, we normally think of PERSON been slow in making its way into the practice of conceptual as rigid; if x is an instance of PERSON, it must be an modeling, although it has been recognized from time to instance of PERSON in every possible world. The STU- time by various communities. In object-oriented languages, DENT property, on the other hand, is normally not rigid; we for example, uniquely identifying an object (as a collection can easily imagine an entity moving in and out of the STU- of data) is critical, in particular when a system has persis- DENT property while being the same individual. This tence or distributed components (Wieringa, De Jonge & notion was later refined in (Guarino, 1998), as shown in Spruit, 1994). In databases, globally unique id’s have been Table 2, where the notion of anti-rigidity was added to gain introduced into most commercial systems to address this φ is a necessary property for all its Rigid φ+R issue. These solutions approach the notion of identity we instances use here, but do not account for it completely, as they Non- φ is not a necessary property of all its merely provide a framework for identifying unique descrip- φ-R Rigid instances tions and not for understanding the nature of the identity φ relationship that holds among the entities they describe.
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